Derive an Expression for a "1/3-Life" for a First-Order Reaction $\frac { \ln \frac { [ \mathrm { A } ] _ { t } } { [ \mathrm {~A} ] _ { 0 } } } { - k }$

Derive an expression for a "1/3-life" for a first-order reaction.

A) $\frac { \ln \frac { [ \mathrm { A } ] _ { t } } { [ \mathrm {~A} ] _ { 0 } } } { - k }$
B) $\frac { 0.462 } { k }$
C) $\frac { \ln \frac { [ \mathrm { A } ] _ { t } } { [ \mathrm {~A} ] _ { 0 } } } { - 3 k }$
D) $\frac { 1.099 } { k }$
E) $\frac { 3 } { k }$